1. Field of the Invention
The present invention relates to a method for displaying a three-dimensional polygon on a screen, wherein a three-dimensional polygon that is geometrically incomplete and thus cannot be displayed on the screen by means of automatic triangulation in a general three-dimensional graphic library can be displayed on the screen. More particularly, the present invention relates to a method for displaying a three-dimensional polygon on a screen, wherein two-dimensional coordinates of vertexes obtained by projecting vertexes of the three-dimensional polygon onto a two-dimensional plane are connected to reconstitute the three-dimensional polygon.
2. Description of the Related Art
There is a recent tendency toward three-dimensional display in a variety of industrial fields including navigation systems for guiding travel paths of vehicles and three-dimensional games. However, in practice, the three-dimensional display is slowly propagated to applicable fields in the entire society due to difficulties in performing three-dimensional modeling operations. This is because it is difficult to apply conventional methods used in many applicable fields, i.e. simple expansion of two-dimensional coordinate data used for two-dimensional display to three-dimensional coordinate data, directly to three-dimensional display. This results from the following limitations on requirements for three-dimensional polygons that can be processed in a general three-dimensional graphic library widely used at present.
First, sides of a three-dimensional polygon should not intersect with each other contrary to that shown in FIG. 1a. That is, the conventional methods support only a simple polygon without an intersection 100.
Second, it is impossible to output a concave polygon with a recessed portion 110 as shown in FIG. 1b, whereas it is possible to output only a convex polygon with outwardly protruding vertexes.
Third, it is impossible to output a polygon with an inner hole 120 as shown in FIG. 1c. 
The reason why there are such limitations on the general three-dimensional graphic library is that, in order to prevent the presence of a polygon with a twisted structure, a list of vertexes of a three-dimensional polygon is subjected to automatic triangulation to reconstitute it into a shape comprising triangles with complete geometric structures in space. For example, if a mesh with a twisted structure as shown in FIG. 2a is subjected to automatic triangulation in a general three-dimensional graphic library, it is caused to be reconstituted into a shape shown in FIG. 2b or 2c. 
FIG. 3a shows errors in automatic triangulation in a general three-dimensional graphic library. It can be understood from FIG. 3 that although an “S”-shaped mesh is intended to be displayed, desired results are not obtained due to the output made by means of automatic triangulation through comparison of all lists of vertexes with one another in a general three-dimensional graphic library.
In this case, the errors are solved by means of a method for finely dividing the mesh as shown in FIG. 3b and performing an input operation again. However, the method for finely dividing a mesh can be hardly used for practical applications since an operator should manually find out a twisted portion in a geometric structure one by one.
FIGS. 4a and 4b are views illustrating results output through automatic triangulation in a general three-dimensional graphic library after simple expansion of map data with two-dimensional coordinates to map data with three-dimensional coordinates in a navigation system. FIG. 4a shows a map obtained by displaying map data with two-dimensional coordinates on a screen, i.e. a map of ‘Han River’ and its peripheral regions. The map data with two-dimensional coordinates were simply expanded to map data with three-dimensional coordinates in the form of (x, y, 0) and then displayed on the screen using a general three-dimensional graphic library. As a result, critical errors occurred in automatic triangulation as shown in FIG. 4b. 
That is, it can be seen that the critical errors in the automatic triangulation severely occurred at ‘Han River’ and its tributaries such as ‘Anyangcheon(Stream)’ and ‘Tancheon(Stream),’ and the like. Since the automatic triangulation is performed to prevent the presence of a twisted structure in space, it is desirable not to perform the automatic triangulation using a general three-dimensional graphic library in case of a map and the like in which all data exist on a single plane.